Summary

This markdown document contains the code and references for the exploratory factor analysis conducted as part of our VIS 2022 Paper submission on a Validated Scale for Aesthetic Pleasure in Visualization

References Considered

Recommendations Extracted From The Literature

Variables to Include

  • at least 3 measured variables are need for statistical identification of a factor
  • recommend 4 - 6 indicators per factor
  • more indicators are preferable

Participants to Include

  • some ratio of the number of variables to the number of factors such as 5:1 or 10:1 or some arbitrary number of participants such as 100 or 200

Distributional Properties of the Data

  • Variability
  • Linearity
  • Normality: reverse negatviely variables
  • Level of Measurement: methodologists have recommended that EFA be based on polychoric correlations if the ordinal variables are measured by fewer than five to seven categories or when distributions of the ordinal variables are asymmetrical
  • Missing Data
  • Outliers: Methods to detect outliers include boxplots and scatterplots for individual variables as well as Mahalanobis distance for multiple variables

Measurement Error

Fabrigar et al. (1999) recommended that variables with reliabilities below .70 should be avoided in EFA. However, adhering to this reliability standard may not be possible when analyzing test items.

#Preparation ## Loading Required Packages

library(png)
library(psych)
library(EFA.dimensions)
library(imager)
## Loading required package: magrittr
## 
## Attaching package: 'imager'
## The following object is masked from 'package:magrittr':
## 
##     add
## The following objects are masked from 'package:stats':
## 
##     convolve, spectrum
## The following object is masked from 'package:graphics':
## 
##     frame
## The following object is masked from 'package:base':
## 
##     save.image
library(corrplot)
## corrplot 0.92 loaded
library(knitr)
library(kableExtra)
library(xtable)
## 
## Attaching package: 'xtable'
## The following objects are masked from 'package:imager':
## 
##     display, label
library(dplyr)
## 
## Attaching package: 'dplyr'
## The following object is masked from 'package:kableExtra':
## 
##     group_rows
## The following objects are masked from 'package:stats':
## 
##     filter, lag
## The following objects are masked from 'package:base':
## 
##     intersect, setdiff, setequal, union
library(tibble)
library(ggplot2)
## 
## Attaching package: 'ggplot2'
## The following objects are masked from 'package:psych':
## 
##     %+%, alpha

Loading Required Files

participantResponseFiles <- list.files(path= "./data",pattern = "\\.csv$") #names correspond to images, one participant per row, one word per column
imageFiles <- list.files(path= "./images",pattern = "\\.png$")

Helper Methods

#Clean the column names
cleanColnames <- function(data){
  newNames <- gsub("^.+?\\.(.+?)\\..*$", "\\1", colnames(data))
  return(newNames)
}

Methods Used in the Analysis

Methods to Test the Appropriateness of the Data for EFA

Correlation

“A subjective method is to examine the correlation matrix. A sizable number of correlations should exceed ±.30 or EFA may be inappropriate”

correlation <- function(num,data){
  
  return(cor(data))
}

Bartlett’s test of sphericity

An objective test of the factorability of the correlation matrix is Bartlett’s (1954) test of sphericity, which statistically tests the hypothesis that the correlation matrix contains ones on the diagonal and zeros on the off-diagonals. Hence, that it was generated by random data. This test should produce a statistically significant chi-square value to justify the application of EFA.

If the p-value from Bartlett’s Test of Sphericity is lower than our chosen significance level (common choices are 0.10, 0.05, and 0.01), then our dataset is suitable for a data reduction technique. (https://www.statology.org/bartletts-test-of-sphericity/)

bartlettTest <- function(num,data){
  bart <- cortest.bartlett(correlation(num,data), n = nrow(data))
  if(bart[2]>0.05) cat("WARNING the p value is above 0.05") else cat("The p value is below 0.05. We are good to continue.")
  cat("\n\n")
  print(bart)
  return(bart)
}

KMO

Large sample sizes make the Bartlett test sensitive to even trivial deviations from randomness, so its results should be supplemented with a measure of sampling adequacy. The Kaiser-Meyer-Olkin (KMO; Kaiser, 1974) measure of sampling adequacy is the ratio of correlations and partial correlations that reflects the extent to which correlations are a function of the variance shared across all variables rather than the variance shared by particular pairs of variables. KMO values range from 0.00 to 1.00 and can be computed for the total correlation matrix as well as for each measured variable.

  • KMO values ≥.70 are desired
  • KMO values ≤.50 are generally considered unacceptable
KMOTest <- function(num,data){
  kmo <- KMO(data)
  cat(paste("The overall measure of sampling adequacy is: ",kmo[1]))
   cat("\n\n")
  if(kmo[1]<.7) cat("WARNING the sampling adequacy has dropped below 0.7") else cat("The sampling adequacy is above 0.7. We are generally good.")
  cat("\n\n")
  return(kmo)
}

The Number of Factors to Retain

Measurement specialists have conducted simulation studies and concluded that parallel analysis and MAP are the most accurate empirical estimates of the number of factors to retain and that scree is a useful subjective adjunct to the empirical estimates. Unfortunately, no method has been found to be correct in all situations, so it is necessary to employ multiple methods and carefully judge each plausible solution to identify the most appropriate factor solution.

parallelAnalysis <- function(num,data){
  
  pdf(paste(paste("generatedPlots-EFA/ScreePlot-Image_",num,sep=""),'.pdf'), width=8, height=4)
  parallel <- fa.parallel(correlation(num,data), n.obs=nrow(data), fa="fa", n.iter=100, main="Scree plots with parallel analysis")
  
  dev.off() 
  cat("\n\n")
}

EFA

Model of Factor Analysis

  • two models: PCA, common factor analysis
  • When the goal of research is to identify latent constructs for theory building or to create measurement instruments in which the researcher wishes to make the case that the resulting measurement instrument reflects a meaningful underlying construct, we argue that common factor analysis (EFA) procedures are usually preferable.
  • this distinction may make little difference when there are ≥40 measured variables

Estimation Method

  • two estimation methods: ML and PA
  • Statistical simulations have found that PA outperforms ML when the relationships between measured variables and factors are relatively weak (≤.40), sample size is relatively small (≤300), multivariate normality is violated, or when the number of factors underlying the measured variables is misspecified
EFA <- function(num, factor, rotation,data){
  efa <- fa(correlation(num,data), nfactors = factor, rotate = rotation, fm = "pa")
  
  #print(xtable(unclass(efa$Structure)),type="html")
  print(efa,sort=TRUE)
  #fa.diagram(efa,cut=.4,digits=2) #I don't fint this diagram particularly useful
  return(efa)
}

Analyzing Participant Responses Per Image

analyze_image <-function(num){
  #First we plot the image that we are analyzing first

  image <- load.image(paste("images/",imageFiles[[num]],sep=""))
  plot(image)
  cat("\n\n")
  
  data <- read.csv(paste("data/",participantResponseFiles[[num]],sep=""), encoding="UTF-8")
  colnames(data) <- cleanColnames(data)

   #Then we go through the analysis steps. These are explained in detail above
   #1. Correlation
  # cat("### Correlation\n")
  # corr <- correlation(num,data)
  # pdf(paste(paste("generatedPlots-EFA/CorrelationMatrix-Image_",num,sep=""),'.pdf'), width=8, height=4)
  #   corrplot(corr, method="square",tl.col="black",title=paste("Correlation for Image ",num),number.cex = 0.5)
  # dev.off()
  # cat("\n\n")
  # 
  # cat("### Bartlett’s test of sphericity\n")
  # bartlettTest(num,data)
  # cat("\n\n")
  # 
  # cat("### KMO\n")
  # KMOTest(num,data)
  # cat("\n\n")
 
  cat("## Scree Plot and Parallel Analysis\n")
  parallelAnalysis(num,data)
  cat("\n\n")

  cat("## Exploratory Factor Analysis - 1 Factor - No Rotation\n")
  efa <- EFA(num, 1, "none",data)
  cat("\n\n")
  # 
  # #Exploratory Analyses below here
  # cat("## Exploratory Factor Analysis - 2 Factors - Varimax Rotation(Orthogonal rotation)\n")
  # EFA(num, 2, "varimax",data )
  # cat("\n\n")
  # 
  # cat("## Exploratory Factor Analysis - 2 Factors - Promax Rotation(Pblique rotation)\n")
  # EFA(num, 2, "promax",data )
  # cat("\n\n")
  
  return(efa)
}
imageCount <- length(participantResponseFiles)
#For debugging we can set the imageCount to whatever we want
#imageCount <- 1
df <- NULL

for (i in 1:imageCount){
   cat(paste(paste("## Image ",i),"\n"))
   efa <- analyze_image(i) #we want to create a big table with all the factor loadings so we'll save the efa results here
   
   if(i == 1){
      df <- as.data.frame(unclass(efa$loadings))
      colnames(df) <- c(paste("PA1 Image ",i))
      df <- tibble::rownames_to_column(df,"terms")
   }
   else{
      dftemp <- as.data.frame(unclass(efa$loadings))
      colnames(dftemp) <- c(paste("PA1 Image ",i))
      dftemp <- tibble::rownames_to_column(dftemp,"terms")
      df <- merge(df,dftemp,by="terms")
   }
}
## ## Image  1
## 
## 
## ## Scree Plot and Parallel Analysis

## Parallel analysis suggests that the number of factors =  2  and the number of components =  NA 
## 
## 
## 
## 
## ## Exploratory Factor Analysis - 1 Factor - No Rotation
## Factor Analysis using method =  pa
## Call: fa(r = correlation(num, data), nfactors = factor, rotate = rotation, 
##     fm = "pa")
## Standardized loadings (pattern matrix) based upon correlation matrix
##                  V  PA1    h2   u2 com
## likable         19 0.91 0.820 0.18   1
## nice            22 0.90 0.818 0.18   1
## enjoyable       13 0.87 0.764 0.24   1
## delightful      10 0.86 0.731 0.27   1
## pleasing        24 0.85 0.721 0.28   1
## appealing        1 0.85 0.719 0.28   1
## pretty          25 0.85 0.716 0.28   1
## lovely          20 0.85 0.716 0.28   1
## beautiful        5 0.84 0.707 0.29   1
## attractive       3 0.84 0.707 0.29   1
## elegant         11 0.83 0.696 0.30   1
## inviting        18 0.83 0.694 0.31   1
## exciting        14 0.79 0.625 0.38   1
## engaging        12 0.79 0.624 0.38   1
## harmonious      16 0.79 0.621 0.38   1
## tasteful        30 0.78 0.615 0.38   1
## satisfying      28 0.77 0.597 0.40   1
## wellDesigned    31 0.76 0.578 0.42   1
## motivating      21 0.74 0.549 0.45   1
## clean            6 0.73 0.527 0.47   1
## interesting     17 0.70 0.495 0.51   1
## balanced         4 0.69 0.480 0.52   1
## sophisticated   29 0.68 0.467 0.53   1
## fascinating     15 0.68 0.458 0.54   1
## colorHarmonious  8 0.65 0.427 0.57   1
## professional    26 0.63 0.400 0.60   1
## organized       23 0.59 0.348 0.65   1
## creative         9 0.53 0.284 0.72   1
## artistic         2 0.52 0.268 0.73   1
## cluttered        7 0.30 0.093 0.91   1
## provoking       27 0.17 0.029 0.97   1
## 
##                  PA1
## SS loadings    17.29
## Proportion Var  0.56
## 
## Mean item complexity =  1
## Test of the hypothesis that 1 factor is sufficient.
## 
## The degrees of freedom for the null model are  465  and the objective function was  29.91
## The degrees of freedom for the model are 434  and the objective function was  5.64 
## 
## The root mean square of the residuals (RMSR) is  0.06 
## The df corrected root mean square of the residuals is  0.06 
## 
## Fit based upon off diagonal values = 0.99
## Measures of factor score adequacy             
##                                                    PA1
## Correlation of (regression) scores with factors   0.99
## Multiple R square of scores with factors          0.98
## Minimum correlation of possible factor scores     0.96
## 
## 
## ## Image  2
## 
## 
## ## Scree Plot and Parallel Analysis

## Parallel analysis suggests that the number of factors =  2  and the number of components =  NA 
## 
## 
## 
## 
## ## Exploratory Factor Analysis - 1 Factor - No Rotation
## Factor Analysis using method =  pa
## Call: fa(r = correlation(num, data), nfactors = factor, rotate = rotation, 
##     fm = "pa")
## Standardized loadings (pattern matrix) based upon correlation matrix
##                  V   PA1    h2   u2 com
## nice            22  0.81 0.653 0.35   1
## pleasing        24  0.80 0.646 0.35   1
## appealing        1  0.80 0.644 0.36   1
## likable         19  0.79 0.619 0.38   1
## enjoyable       13  0.78 0.609 0.39   1
## attractive       3  0.78 0.601 0.40   1
## beautiful        5  0.77 0.587 0.41   1
## elegant         11  0.76 0.572 0.43   1
## pretty          25  0.76 0.571 0.43   1
## lovely          20  0.75 0.560 0.44   1
## delightful      10  0.74 0.553 0.45   1
## inviting        18  0.74 0.541 0.46   1
## satisfying      28  0.73 0.540 0.46   1
## wellDesigned    31  0.71 0.499 0.50   1
## interesting     17  0.70 0.494 0.51   1
## engaging        12  0.70 0.490 0.51   1
## clean            6  0.70 0.484 0.52   1
## harmonious      16  0.69 0.477 0.52   1
## professional    26  0.67 0.450 0.55   1
## exciting        14  0.66 0.440 0.56   1
## motivating      21  0.65 0.424 0.58   1
## tasteful        30  0.64 0.414 0.59   1
## fascinating     15  0.64 0.413 0.59   1
## balanced         4  0.63 0.394 0.61   1
## sophisticated   29  0.63 0.391 0.61   1
## organized       23  0.61 0.378 0.62   1
## colorHarmonious  8  0.59 0.349 0.65   1
## artistic         2  0.49 0.241 0.76   1
## creative         9  0.49 0.240 0.76   1
## cluttered        7 -0.33 0.108 0.89   1
## provoking       27  0.20 0.039 0.96   1
## 
##                  PA1
## SS loadings    14.42
## Proportion Var  0.47
## 
## Mean item complexity =  1
## Test of the hypothesis that 1 factor is sufficient.
## 
## The degrees of freedom for the null model are  465  and the objective function was  23.71
## The degrees of freedom for the model are 434  and the objective function was  6.68 
## 
## The root mean square of the residuals (RMSR) is  0.09 
## The df corrected root mean square of the residuals is  0.09 
## 
## Fit based upon off diagonal values = 0.97
## Measures of factor score adequacy             
##                                                    PA1
## Correlation of (regression) scores with factors   0.98
## Multiple R square of scores with factors          0.97
## Minimum correlation of possible factor scores     0.94
## 
## 
## ## Image  3
## 
## 
## ## Scree Plot and Parallel Analysis
## Parallel analysis suggests that the number of factors =  2  and the number of components =  NA 
## 
## 
## 
## 
## ## Exploratory Factor Analysis - 1 Factor - No Rotation
## Factor Analysis using method =  pa
## Call: fa(r = correlation(num, data), nfactors = factor, rotate = rotation, 
##     fm = "pa")
## Standardized loadings (pattern matrix) based upon correlation matrix
##                  V  PA1    h2   u2 com
## likable         19 0.88 0.770 0.23   1
## pleasing        24 0.84 0.699 0.30   1
## enjoyable       13 0.83 0.695 0.30   1
## attractive       3 0.81 0.658 0.34   1
## nice            22 0.81 0.651 0.35   1
## appealing        1 0.80 0.637 0.36   1
## lovely          20 0.78 0.602 0.40   1
## delightful      10 0.78 0.601 0.40   1
## pretty          25 0.77 0.599 0.40   1
## satisfying      28 0.77 0.590 0.41   1
## engaging        12 0.76 0.579 0.42   1
## harmonious      16 0.76 0.578 0.42   1
## beautiful        5 0.76 0.576 0.42   1
## fascinating     15 0.73 0.538 0.46   1
## exciting        14 0.72 0.526 0.47   1
## motivating      21 0.71 0.511 0.49   1
## inviting        18 0.71 0.509 0.49   1
## clean            6 0.71 0.507 0.49   1
## interesting     17 0.71 0.502 0.50   1
## elegant         11 0.71 0.500 0.50   1
## tasteful        30 0.68 0.466 0.53   1
## wellDesigned    31 0.67 0.446 0.55   1
## colorHarmonious  8 0.63 0.400 0.60   1
## sophisticated   29 0.62 0.387 0.61   1
## organized       23 0.62 0.384 0.62   1
## balanced         4 0.61 0.376 0.62   1
## creative         9 0.55 0.306 0.69   1
## professional    26 0.52 0.268 0.73   1
## artistic         2 0.51 0.259 0.74   1
## provoking       27 0.22 0.047 0.95   1
## cluttered        7 0.03 0.001 1.00   1
## 
##                  PA1
## SS loadings    15.17
## Proportion Var  0.49
## 
## Mean item complexity =  1
## Test of the hypothesis that 1 factor is sufficient.
## 
## The degrees of freedom for the null model are  465  and the objective function was  24.45
## The degrees of freedom for the model are 434  and the objective function was  5.55 
## 
## The root mean square of the residuals (RMSR) is  0.06 
## The df corrected root mean square of the residuals is  0.07 
## 
## Fit based upon off diagonal values = 0.98
## Measures of factor score adequacy             
##                                                    PA1
## Correlation of (regression) scores with factors   0.99
## Multiple R square of scores with factors          0.97
## Minimum correlation of possible factor scores     0.95
## 
## 
## ## Image  4
## Warning in readfun(f, ...): libpng warning: iCCP: known incorrect sRGB profile

## 
## 
## ## Scree Plot and Parallel Analysis

## Parallel analysis suggests that the number of factors =  3  and the number of components =  NA 
## 
## 
## 
## 
## ## Exploratory Factor Analysis - 1 Factor - No Rotation
## Factor Analysis using method =  pa
## Call: fa(r = correlation(num, data), nfactors = factor, rotate = rotation, 
##     fm = "pa")
## Standardized loadings (pattern matrix) based upon correlation matrix
##                  V  PA1    h2   u2 com
## pleasing        24 0.88 0.774 0.23   1
## likable         19 0.87 0.752 0.25   1
## enjoyable       13 0.86 0.741 0.26   1
## delightful      10 0.85 0.716 0.28   1
## appealing        1 0.84 0.711 0.29   1
## satisfying      28 0.83 0.696 0.30   1
## nice            22 0.82 0.677 0.32   1
## lovely          20 0.82 0.670 0.33   1
## attractive       3 0.81 0.658 0.34   1
## beautiful        5 0.79 0.626 0.37   1
## pretty          25 0.78 0.607 0.39   1
## elegant         11 0.78 0.604 0.40   1
## wellDesigned    31 0.77 0.589 0.41   1
## fascinating     15 0.77 0.588 0.41   1
## motivating      21 0.77 0.587 0.41   1
## exciting        14 0.76 0.582 0.42   1
## harmonious      16 0.75 0.559 0.44   1
## engaging        12 0.74 0.553 0.45   1
## interesting     17 0.74 0.544 0.46   1
## organized       23 0.74 0.541 0.46   1
## balanced         4 0.73 0.539 0.46   1
## inviting        18 0.73 0.535 0.47   1
## tasteful        30 0.72 0.518 0.48   1
## clean            6 0.64 0.413 0.59   1
## sophisticated   29 0.63 0.403 0.60   1
## colorHarmonious  8 0.63 0.403 0.60   1
## professional    26 0.61 0.374 0.63   1
## creative         9 0.60 0.362 0.64   1
## artistic         2 0.59 0.347 0.65   1
## provoking       27 0.28 0.081 0.92   1
## cluttered        7 0.15 0.022 0.98   1
## 
##                  PA1
## SS loadings    16.77
## Proportion Var  0.54
## 
## Mean item complexity =  1
## Test of the hypothesis that 1 factor is sufficient.
## 
## The degrees of freedom for the null model are  465  and the objective function was  28.05
## The degrees of freedom for the model are 434  and the objective function was  5.73 
## 
## The root mean square of the residuals (RMSR) is  0.06 
## The df corrected root mean square of the residuals is  0.06 
## 
## Fit based upon off diagonal values = 0.99
## Measures of factor score adequacy             
##                                                    PA1
## Correlation of (regression) scores with factors   0.99
## Multiple R square of scores with factors          0.98
## Minimum correlation of possible factor scores     0.96
## 
## 
## ## Image  5
## 
## 
## ## Scree Plot and Parallel Analysis

## Parallel analysis suggests that the number of factors =  2  and the number of components =  NA 
## 
## 
## 
## 
## ## Exploratory Factor Analysis - 1 Factor - No Rotation
## Factor Analysis using method =  pa
## Call: fa(r = correlation(num, data), nfactors = factor, rotate = rotation, 
##     fm = "pa")
## Standardized loadings (pattern matrix) based upon correlation matrix
##                  V  PA1    h2   u2 com
## pleasing        24 0.89 0.792 0.21   1
## nice            22 0.87 0.766 0.23   1
## appealing        1 0.87 0.750 0.25   1
## likable         19 0.86 0.746 0.25   1
## enjoyable       13 0.86 0.746 0.25   1
## attractive       3 0.86 0.743 0.26   1
## satisfying      28 0.85 0.725 0.28   1
## beautiful        5 0.84 0.698 0.30   1
## delightful      10 0.83 0.689 0.31   1
## motivating      21 0.83 0.685 0.31   1
## inviting        18 0.82 0.675 0.32   1
## harmonious      16 0.82 0.675 0.33   1
## exciting        14 0.81 0.663 0.34   1
## wellDesigned    31 0.81 0.657 0.34   1
## pretty          25 0.81 0.652 0.35   1
## lovely          20 0.80 0.637 0.36   1
## engaging        12 0.78 0.613 0.39   1
## tasteful        30 0.77 0.587 0.41   1
## interesting     17 0.76 0.577 0.42   1
## elegant         11 0.74 0.544 0.46   1
## balanced         4 0.71 0.510 0.49   1
## clean            6 0.70 0.489 0.51   1
## fascinating     15 0.70 0.486 0.51   1
## organized       23 0.67 0.454 0.55   1
## creative         9 0.67 0.450 0.55   1
## artistic         2 0.66 0.432 0.57   1
## colorHarmonious  8 0.64 0.405 0.59   1
## professional    26 0.62 0.382 0.62   1
## sophisticated   29 0.61 0.368 0.63   1
## cluttered        7 0.39 0.150 0.85   1
## provoking       27 0.28 0.079 0.92   1
## 
##                  PA1
## SS loadings    17.83
## Proportion Var  0.58
## 
## Mean item complexity =  1
## Test of the hypothesis that 1 factor is sufficient.
## 
## The degrees of freedom for the null model are  465  and the objective function was  30.56
## The degrees of freedom for the model are 434  and the objective function was  5.71 
## 
## The root mean square of the residuals (RMSR) is  0.06 
## The df corrected root mean square of the residuals is  0.06 
## 
## Fit based upon off diagonal values = 0.99
## Measures of factor score adequacy             
##                                                    PA1
## Correlation of (regression) scores with factors   0.99
## Multiple R square of scores with factors          0.98
## Minimum correlation of possible factor scores     0.96
## 
## 
## ## Image  6
## 
## 
## ## Scree Plot and Parallel Analysis

## Parallel analysis suggests that the number of factors =  2  and the number of components =  NA 
## 
## 
## 
## 
## ## Exploratory Factor Analysis - 1 Factor - No Rotation
## Factor Analysis using method =  pa
## Call: fa(r = correlation(num, data), nfactors = factor, rotate = rotation, 
##     fm = "pa")
## Standardized loadings (pattern matrix) based upon correlation matrix
##                  V  PA1    h2   u2 com
## pleasing        24 0.87 0.763 0.24   1
## attractive       3 0.87 0.755 0.24   1
## likable         19 0.84 0.706 0.29   1
## enjoyable       13 0.84 0.702 0.30   1
## nice            22 0.83 0.687 0.31   1
## appealing        1 0.83 0.687 0.31   1
## delightful      10 0.81 0.658 0.34   1
## pretty          25 0.81 0.657 0.34   1
## satisfying      28 0.80 0.645 0.35   1
## inviting        18 0.80 0.639 0.36   1
## tasteful        30 0.78 0.611 0.39   1
## motivating      21 0.78 0.611 0.39   1
## engaging        12 0.78 0.604 0.40   1
## beautiful        5 0.78 0.601 0.40   1
## lovely          20 0.77 0.590 0.41   1
## exciting        14 0.76 0.574 0.43   1
## harmonious      16 0.74 0.554 0.45   1
## wellDesigned    31 0.73 0.534 0.47   1
## fascinating     15 0.72 0.519 0.48   1
## interesting     17 0.71 0.509 0.49   1
## balanced         4 0.69 0.483 0.52   1
## elegant         11 0.68 0.457 0.54   1
## colorHarmonious  8 0.63 0.395 0.60   1
## artistic         2 0.63 0.395 0.61   1
## sophisticated   29 0.62 0.390 0.61   1
## creative         9 0.62 0.386 0.61   1
## clean            6 0.60 0.363 0.64   1
## organized       23 0.59 0.345 0.65   1
## professional    26 0.53 0.282 0.72   1
## provoking       27 0.33 0.108 0.89   1
## cluttered        7 0.18 0.033 0.97   1
## 
##                  PA1
## SS loadings    16.24
## Proportion Var  0.52
## 
## Mean item complexity =  1
## Test of the hypothesis that 1 factor is sufficient.
## 
## The degrees of freedom for the null model are  465  and the objective function was  27.12
## The degrees of freedom for the model are 434  and the objective function was  5.91 
## 
## The root mean square of the residuals (RMSR) is  0.07 
## The df corrected root mean square of the residuals is  0.07 
## 
## Fit based upon off diagonal values = 0.98
## Measures of factor score adequacy             
##                                                    PA1
## Correlation of (regression) scores with factors   0.99
## Multiple R square of scores with factors          0.98
## Minimum correlation of possible factor scores     0.95
## 
## 
## ## Image  7
## 
## 
## ## Scree Plot and Parallel Analysis

## Parallel analysis suggests that the number of factors =  3  and the number of components =  NA 
## 
## 
## 
## 
## ## Exploratory Factor Analysis - 1 Factor - No Rotation
## Factor Analysis using method =  pa
## Call: fa(r = correlation(num, data), nfactors = factor, rotate = rotation, 
##     fm = "pa")
## Standardized loadings (pattern matrix) based upon correlation matrix
##                  V  PA1    h2   u2 com
## satisfying      28 0.90 0.813 0.19   1
## likable         19 0.90 0.807 0.19   1
## pleasing        24 0.90 0.803 0.20   1
## attractive       3 0.89 0.795 0.20   1
## delightful      10 0.89 0.787 0.21   1
## enjoyable       13 0.88 0.781 0.22   1
## pretty          25 0.88 0.773 0.23   1
## appealing        1 0.88 0.767 0.23   1
## beautiful        5 0.87 0.761 0.24   1
## nice            22 0.87 0.760 0.24   1
## motivating      21 0.84 0.706 0.29   1
## inviting        18 0.84 0.703 0.30   1
## lovely          20 0.83 0.693 0.31   1
## elegant         11 0.83 0.691 0.31   1
## engaging        12 0.82 0.674 0.33   1
## exciting        14 0.81 0.657 0.34   1
## fascinating     15 0.80 0.647 0.35   1
## tasteful        30 0.80 0.642 0.36   1
## harmonious      16 0.74 0.550 0.45   1
## sophisticated   29 0.73 0.529 0.47   1
## interesting     17 0.73 0.527 0.47   1
## artistic         2 0.69 0.471 0.53   1
## wellDesigned    31 0.69 0.471 0.53   1
## clean            6 0.66 0.432 0.57   1
## creative         9 0.66 0.430 0.57   1
## professional    26 0.60 0.355 0.64   1
## balanced         4 0.59 0.344 0.66   1
## organized       23 0.55 0.304 0.70   1
## colorHarmonious  8 0.48 0.227 0.77   1
## cluttered        7 0.27 0.072 0.93   1
## provoking       27 0.19 0.037 0.96   1
## 
##                  PA1
## SS loadings    18.01
## Proportion Var  0.58
## 
## Mean item complexity =  1
## Test of the hypothesis that 1 factor is sufficient.
## 
## The degrees of freedom for the null model are  465  and the objective function was  33.25
## The degrees of freedom for the model are 434  and the objective function was  6.4 
## 
## The root mean square of the residuals (RMSR) is  0.06 
## The df corrected root mean square of the residuals is  0.06 
## 
## Fit based upon off diagonal values = 0.99
## Measures of factor score adequacy             
##                                                    PA1
## Correlation of (regression) scores with factors   0.99
## Multiple R square of scores with factors          0.98
## Minimum correlation of possible factor scores     0.97
## 
## 
## ## Image  8
## 
## 
## ## Scree Plot and Parallel Analysis

## Parallel analysis suggests that the number of factors =  2  and the number of components =  NA 
## 
## 
## 
## 
## ## Exploratory Factor Analysis - 1 Factor - No Rotation
## Factor Analysis using method =  pa
## Call: fa(r = correlation(num, data), nfactors = factor, rotate = rotation, 
##     fm = "pa")
## Standardized loadings (pattern matrix) based upon correlation matrix
##                  V  PA1   h2   u2 com
## likable         19 0.88 0.77 0.23   1
## enjoyable       13 0.87 0.76 0.24   1
## nice            22 0.87 0.76 0.24   1
## inviting        18 0.85 0.72 0.28   1
## appealing        1 0.85 0.72 0.28   1
## pleasing        24 0.84 0.71 0.29   1
## attractive       3 0.84 0.70 0.30   1
## engaging        12 0.83 0.69 0.31   1
## delightful      10 0.82 0.67 0.33   1
## lovely          20 0.81 0.66 0.34   1
## beautiful        5 0.81 0.65 0.35   1
## tasteful        30 0.81 0.65 0.35   1
## satisfying      28 0.80 0.65 0.35   1
## pretty          25 0.79 0.63 0.37   1
## exciting        14 0.77 0.59 0.41   1
## motivating      21 0.75 0.56 0.44   1
## interesting     17 0.74 0.55 0.45   1
## harmonious      16 0.74 0.55 0.45   1
## fascinating     15 0.71 0.50 0.50   1
## wellDesigned    31 0.71 0.50 0.50   1
## balanced         4 0.70 0.49 0.51   1
## creative         9 0.70 0.48 0.52   1
## clean            6 0.70 0.48 0.52   1
## elegant         11 0.69 0.47 0.53   1
## sophisticated   29 0.65 0.43 0.57   1
## artistic         2 0.61 0.37 0.63   1
## organized       23 0.60 0.36 0.64   1
## colorHarmonious  8 0.55 0.30 0.70   1
## professional    26 0.46 0.21 0.79   1
## provoking       27 0.37 0.14 0.86   1
## cluttered        7 0.34 0.11 0.89   1
## 
##                  PA1
## SS loadings    16.86
## Proportion Var  0.54
## 
## Mean item complexity =  1
## Test of the hypothesis that 1 factor is sufficient.
## 
## The degrees of freedom for the null model are  465  and the objective function was  28.96
## The degrees of freedom for the model are 434  and the objective function was  6.18 
## 
## The root mean square of the residuals (RMSR) is  0.06 
## The df corrected root mean square of the residuals is  0.07 
## 
## Fit based upon off diagonal values = 0.99
## Measures of factor score adequacy             
##                                                    PA1
## Correlation of (regression) scores with factors   0.99
## Multiple R square of scores with factors          0.98
## Minimum correlation of possible factor scores     0.96
## 
## 
## ## Image  9
## 
## 
## ## Scree Plot and Parallel Analysis

## Parallel analysis suggests that the number of factors =  3  and the number of components =  NA 
## 
## 
## 
## 
## ## Exploratory Factor Analysis - 1 Factor - No Rotation
## Factor Analysis using method =  pa
## Call: fa(r = correlation(num, data), nfactors = factor, rotate = rotation, 
##     fm = "pa")
## Standardized loadings (pattern matrix) based upon correlation matrix
##                  V  PA1   h2   u2 com
## appealing        1 0.85 0.72 0.28   1
## attractive       3 0.84 0.71 0.29   1
## enjoyable       13 0.84 0.71 0.29   1
## likable         19 0.84 0.71 0.29   1
## satisfying      28 0.82 0.68 0.32   1
## nice            22 0.81 0.66 0.34   1
## tasteful        30 0.81 0.65 0.35   1
## pleasing        24 0.80 0.65 0.35   1
## delightful      10 0.79 0.62 0.38   1
## inviting        18 0.78 0.61 0.39   1
## pretty          25 0.76 0.58 0.42   1
## beautiful        5 0.76 0.57 0.43   1
## motivating      21 0.75 0.56 0.44   1
## lovely          20 0.74 0.54 0.46   1
## engaging        12 0.74 0.54 0.46   1
## wellDesigned    31 0.73 0.53 0.47   1
## fascinating     15 0.72 0.51 0.49   1
## elegant         11 0.71 0.50 0.50   1
## exciting        14 0.70 0.49 0.51   1
## harmonious      16 0.69 0.48 0.52   1
## sophisticated   29 0.66 0.43 0.57   1
## balanced         4 0.65 0.42 0.58   1
## creative         9 0.62 0.39 0.61   1
## interesting     17 0.61 0.37 0.63   1
## clean            6 0.60 0.36 0.64   1
## organized       23 0.59 0.35 0.65   1
## artistic         2 0.56 0.32 0.68   1
## professional    26 0.50 0.25 0.75   1
## colorHarmonious  8 0.43 0.19 0.81   1
## cluttered        7 0.41 0.17 0.83   1
## provoking       27 0.32 0.10 0.90   1
## 
##                  PA1
## SS loadings    15.38
## Proportion Var  0.50
## 
## Mean item complexity =  1
## Test of the hypothesis that 1 factor is sufficient.
## 
## The degrees of freedom for the null model are  465  and the objective function was  25.71
## The degrees of freedom for the model are 434  and the objective function was  6.37 
## 
## The root mean square of the residuals (RMSR) is  0.07 
## The df corrected root mean square of the residuals is  0.07 
## 
## Fit based upon off diagonal values = 0.98
## Measures of factor score adequacy             
##                                                    PA1
## Correlation of (regression) scores with factors   0.99
## Multiple R square of scores with factors          0.97
## Minimum correlation of possible factor scores     0.95
## 
## 
## ## Image  10
## 
## 
## ## Scree Plot and Parallel Analysis

## Parallel analysis suggests that the number of factors =  2  and the number of components =  NA 
## 
## 
## 
## 
## ## Exploratory Factor Analysis - 1 Factor - No Rotation
## Factor Analysis using method =  pa
## Call: fa(r = correlation(num, data), nfactors = factor, rotate = rotation, 
##     fm = "pa")
## Standardized loadings (pattern matrix) based upon correlation matrix
##                  V  PA1    h2   u2 com
## appealing        1 0.88 0.772 0.23   1
## pleasing        24 0.88 0.770 0.23   1
## enjoyable       13 0.87 0.755 0.25   1
## likable         19 0.86 0.736 0.26   1
## attractive       3 0.86 0.733 0.27   1
## nice            22 0.85 0.718 0.28   1
## satisfying      28 0.85 0.717 0.28   1
## elegant         11 0.84 0.707 0.29   1
## beautiful        5 0.82 0.678 0.32   1
## delightful      10 0.82 0.670 0.33   1
## lovely          20 0.81 0.661 0.34   1
## tasteful        30 0.80 0.642 0.36   1
## pretty          25 0.80 0.642 0.36   1
## harmonious      16 0.80 0.638 0.36   1
## inviting        18 0.78 0.613 0.39   1
## balanced         4 0.77 0.599 0.40   1
## motivating      21 0.77 0.595 0.40   1
## exciting        14 0.77 0.586 0.41   1
## engaging        12 0.76 0.578 0.42   1
## wellDesigned    31 0.74 0.546 0.45   1
## creative         9 0.68 0.464 0.54   1
## clean            6 0.68 0.458 0.54   1
## artistic         2 0.66 0.439 0.56   1
## fascinating     15 0.66 0.436 0.56   1
## organized       23 0.66 0.433 0.57   1
## interesting     17 0.64 0.412 0.59   1
## sophisticated   29 0.63 0.395 0.61   1
## colorHarmonious  8 0.62 0.379 0.62   1
## professional    26 0.61 0.375 0.62   1
## cluttered        7 0.45 0.199 0.80   1
## provoking       27 0.27 0.075 0.92   1
## 
##                  PA1
## SS loadings    17.42
## Proportion Var  0.56
## 
## Mean item complexity =  1
## Test of the hypothesis that 1 factor is sufficient.
## 
## The degrees of freedom for the null model are  465  and the objective function was  29.01
## The degrees of freedom for the model are 434  and the objective function was  5.16 
## 
## The root mean square of the residuals (RMSR) is  0.05 
## The df corrected root mean square of the residuals is  0.06 
## 
## Fit based upon off diagonal values = 0.99
## Measures of factor score adequacy             
##                                                    PA1
## Correlation of (regression) scores with factors   0.99
## Multiple R square of scores with factors          0.98
## Minimum correlation of possible factor scores     0.96
## 
## 
## ## Image  11
## 
## 
## ## Scree Plot and Parallel Analysis

## Parallel analysis suggests that the number of factors =  2  and the number of components =  NA 
## 
## 
## 
## 
## ## Exploratory Factor Analysis - 1 Factor - No Rotation
## Factor Analysis using method =  pa
## Call: fa(r = correlation(num, data), nfactors = factor, rotate = rotation, 
##     fm = "pa")
## Standardized loadings (pattern matrix) based upon correlation matrix
##                  V  PA1    h2   u2 com
## pleasing        24 0.87 0.756 0.24   1
## delightful      10 0.86 0.738 0.26   1
## lovely          20 0.86 0.732 0.27   1
## satisfying      28 0.86 0.731 0.27   1
## enjoyable       13 0.85 0.728 0.27   1
## appealing        1 0.85 0.725 0.27   1
## likable         19 0.85 0.721 0.28   1
## beautiful        5 0.85 0.718 0.28   1
## attractive       3 0.85 0.715 0.29   1
## nice            22 0.84 0.708 0.29   1
## pretty          25 0.84 0.698 0.30   1
## inviting        18 0.83 0.696 0.30   1
## exciting        14 0.82 0.674 0.33   1
## tasteful        30 0.82 0.669 0.33   1
## engaging        12 0.79 0.630 0.37   1
## motivating      21 0.78 0.615 0.38   1
## harmonious      16 0.77 0.596 0.40   1
## wellDesigned    31 0.76 0.571 0.43   1
## elegant         11 0.76 0.571 0.43   1
## balanced         4 0.74 0.543 0.46   1
## fascinating     15 0.73 0.531 0.47   1
## clean            6 0.71 0.504 0.50   1
## interesting     17 0.70 0.490 0.51   1
## creative         9 0.65 0.424 0.58   1
## artistic         2 0.64 0.416 0.58   1
## organized       23 0.64 0.409 0.59   1
## sophisticated   29 0.63 0.398 0.60   1
## professional    26 0.52 0.273 0.73   1
## colorHarmonious  8 0.51 0.257 0.74   1
## provoking       27 0.40 0.162 0.84   1
## cluttered        7 0.21 0.043 0.96   1
## 
##                  PA1
## SS loadings    17.44
## Proportion Var  0.56
## 
## Mean item complexity =  1
## Test of the hypothesis that 1 factor is sufficient.
## 
## The degrees of freedom for the null model are  465  and the objective function was  30.52
## The degrees of freedom for the model are 434  and the objective function was  6.32 
## 
## The root mean square of the residuals (RMSR) is  0.06 
## The df corrected root mean square of the residuals is  0.07 
## 
## Fit based upon off diagonal values = 0.99
## Measures of factor score adequacy             
##                                                    PA1
## Correlation of (regression) scores with factors   0.99
## Multiple R square of scores with factors          0.98
## Minimum correlation of possible factor scores     0.96
## 
## 
## ## Image  12
## 
## 
## ## Scree Plot and Parallel Analysis

## Parallel analysis suggests that the number of factors =  3  and the number of components =  NA 
## 
## 
## 
## 
## ## Exploratory Factor Analysis - 1 Factor - No Rotation
## Factor Analysis using method =  pa
## Call: fa(r = correlation(num, data), nfactors = factor, rotate = rotation, 
##     fm = "pa")
## Standardized loadings (pattern matrix) based upon correlation matrix
##                  V   PA1     h2   u2 com
## likable         19  0.89 0.7856 0.21   1
## pleasing        24  0.88 0.7768 0.22   1
## enjoyable       13  0.88 0.7728 0.23   1
## delightful      10  0.88 0.7665 0.23   1
## appealing        1  0.88 0.7658 0.23   1
## satisfying      28  0.87 0.7625 0.24   1
## attractive       3  0.87 0.7591 0.24   1
## lovely          20  0.86 0.7360 0.26   1
## beautiful        5  0.85 0.7302 0.27   1
## pretty          25  0.85 0.7196 0.28   1
## nice            22  0.82 0.6727 0.33   1
## wellDesigned    31  0.81 0.6639 0.34   1
## elegant         11  0.80 0.6454 0.35   1
## harmonious      16  0.80 0.6356 0.36   1
## inviting        18  0.78 0.6007 0.40   1
## fascinating     15  0.77 0.5983 0.40   1
## exciting        14  0.77 0.5939 0.41   1
## engaging        12  0.77 0.5864 0.41   1
## tasteful        30  0.76 0.5750 0.42   1
## sophisticated   29  0.75 0.5642 0.44   1
## interesting     17  0.73 0.5309 0.47   1
## motivating      21  0.71 0.5097 0.49   1
## clean            6  0.71 0.5007 0.50   1
## artistic         2  0.69 0.4813 0.52   1
## professional    26  0.67 0.4544 0.55   1
## balanced         4  0.66 0.4393 0.56   1
## organized       23  0.66 0.4316 0.57   1
## creative         9  0.64 0.4139 0.59   1
## colorHarmonious  8  0.62 0.3830 0.62   1
## provoking       27  0.32 0.1052 0.89   1
## cluttered        7 -0.05 0.0025 1.00   1
## 
##                  PA1
## SS loadings    17.96
## Proportion Var  0.58
## 
## Mean item complexity =  1
## Test of the hypothesis that 1 factor is sufficient.
## 
## The degrees of freedom for the null model are  465  and the objective function was  31.16
## The degrees of freedom for the model are 434  and the objective function was  5.62 
## 
## The root mean square of the residuals (RMSR) is  0.06 
## The df corrected root mean square of the residuals is  0.06 
## 
## Fit based upon off diagonal values = 0.99
## Measures of factor score adequacy             
##                                                    PA1
## Correlation of (regression) scores with factors   0.99
## Multiple R square of scores with factors          0.98
## Minimum correlation of possible factor scores     0.96
## 
## 
## ## Image  13
## 
## 
## ## Scree Plot and Parallel Analysis

## Parallel analysis suggests that the number of factors =  2  and the number of components =  NA 
## 
## 
## 
## 
## ## Exploratory Factor Analysis - 1 Factor - No Rotation
## Factor Analysis using method =  pa
## Call: fa(r = correlation(num, data), nfactors = factor, rotate = rotation, 
##     fm = "pa")
## Standardized loadings (pattern matrix) based upon correlation matrix
##                  V  PA1    h2   u2 com
## nice            22 0.89 0.795 0.21   1
## delightful      10 0.89 0.792 0.21   1
## appealing        1 0.88 0.777 0.22   1
## likable         19 0.87 0.759 0.24   1
## pleasing        24 0.87 0.759 0.24   1
## attractive       3 0.86 0.732 0.27   1
## satisfying      28 0.85 0.729 0.27   1
## inviting        18 0.84 0.702 0.30   1
## enjoyable       13 0.83 0.696 0.30   1
## motivating      21 0.83 0.690 0.31   1
## lovely          20 0.83 0.683 0.32   1
## pretty          25 0.83 0.681 0.32   1
## tasteful        30 0.81 0.663 0.34   1
## wellDesigned    31 0.81 0.653 0.35   1
## engaging        12 0.80 0.646 0.35   1
## exciting        14 0.79 0.617 0.38   1
## elegant         11 0.78 0.616 0.38   1
## beautiful        5 0.78 0.615 0.38   1
## harmonious      16 0.76 0.582 0.42   1
## fascinating     15 0.76 0.576 0.42   1
## interesting     17 0.74 0.543 0.46   1
## sophisticated   29 0.71 0.503 0.50   1
## balanced         4 0.68 0.463 0.54   1
## professional    26 0.67 0.455 0.54   1
## organized       23 0.65 0.428 0.57   1
## clean            6 0.63 0.391 0.61   1
## creative         9 0.58 0.333 0.67   1
## artistic         2 0.55 0.304 0.70   1
## colorHarmonious  8 0.43 0.184 0.82   1
## provoking       27 0.22 0.049 0.95   1
## cluttered        7 0.12 0.015 0.99   1
## 
##                  PA1
## SS loadings    17.43
## Proportion Var  0.56
## 
## Mean item complexity =  1
## Test of the hypothesis that 1 factor is sufficient.
## 
## The degrees of freedom for the null model are  465  and the objective function was  30.41
## The degrees of freedom for the model are 434  and the objective function was  5.77 
## 
## The root mean square of the residuals (RMSR) is  0.06 
## The df corrected root mean square of the residuals is  0.06 
## 
## Fit based upon off diagonal values = 0.99
## Measures of factor score adequacy             
##                                                    PA1
## Correlation of (regression) scores with factors   0.99
## Multiple R square of scores with factors          0.98
## Minimum correlation of possible factor scores     0.96
## 
## 
## ## Image  14
## 
## 
## ## Scree Plot and Parallel Analysis

## Parallel analysis suggests that the number of factors =  2  and the number of components =  NA 
## 
## 
## 
## 
## ## Exploratory Factor Analysis - 1 Factor - No Rotation
## Factor Analysis using method =  pa
## Call: fa(r = correlation(num, data), nfactors = factor, rotate = rotation, 
##     fm = "pa")
## Standardized loadings (pattern matrix) based upon correlation matrix
##                  V  PA1     h2   u2 com
## likable         19 0.87 0.7587 0.24   1
## pretty          25 0.86 0.7423 0.26   1
## enjoyable       13 0.85 0.7269 0.27   1
## pleasing        24 0.84 0.7137 0.29   1
## attractive       3 0.84 0.7086 0.29   1
## delightful      10 0.84 0.7038 0.30   1
## appealing        1 0.83 0.6810 0.32   1
## nice            22 0.82 0.6775 0.32   1
## beautiful        5 0.82 0.6655 0.33   1
## satisfying      28 0.81 0.6585 0.34   1
## lovely          20 0.79 0.6310 0.37   1
## tasteful        30 0.77 0.5945 0.41   1
## motivating      21 0.76 0.5810 0.42   1
## inviting        18 0.76 0.5741 0.43   1
## harmonious      16 0.75 0.5699 0.43   1
## exciting        14 0.75 0.5672 0.43   1
## elegant         11 0.74 0.5485 0.45   1
## engaging        12 0.73 0.5393 0.46   1
## clean            6 0.73 0.5376 0.46   1
## balanced         4 0.71 0.5081 0.49   1
## sophisticated   29 0.71 0.5031 0.50   1
## fascinating     15 0.70 0.4908 0.51   1
## wellDesigned    31 0.66 0.4296 0.57   1
## colorHarmonious  8 0.64 0.4133 0.59   1
## organized       23 0.62 0.3901 0.61   1
## professional    26 0.62 0.3845 0.62   1
## interesting     17 0.59 0.3440 0.66   1
## artistic         2 0.58 0.3351 0.66   1
## creative         9 0.54 0.2940 0.71   1
## provoking       27 0.22 0.0492 0.95   1
## cluttered        7 0.05 0.0021 1.00   1
## 
##                  PA1
## SS loadings    16.32
## Proportion Var  0.53
## 
## Mean item complexity =  1
## Test of the hypothesis that 1 factor is sufficient.
## 
## The degrees of freedom for the null model are  465  and the objective function was  27.59
## The degrees of freedom for the model are 434  and the objective function was  5.94 
## 
## The root mean square of the residuals (RMSR) is  0.06 
## The df corrected root mean square of the residuals is  0.07 
## 
## Fit based upon off diagonal values = 0.99
## Measures of factor score adequacy             
##                                                    PA1
## Correlation of (regression) scores with factors   0.99
## Multiple R square of scores with factors          0.98
## Minimum correlation of possible factor scores     0.95
## 
## 
## ## Image  15
## 
## 
## ## Scree Plot and Parallel Analysis

## Parallel analysis suggests that the number of factors =  2  and the number of components =  NA 
## 
## 
## 
## 
## ## Exploratory Factor Analysis - 1 Factor - No Rotation
## Factor Analysis using method =  pa
## Call: fa(r = correlation(num, data), nfactors = factor, rotate = rotation, 
##     fm = "pa")
## Standardized loadings (pattern matrix) based upon correlation matrix
##                  V  PA1    h2   u2 com
## appealing        1 0.90 0.813 0.19   1
## nice            22 0.89 0.795 0.20   1
## likable         19 0.89 0.794 0.21   1
## enjoyable       13 0.89 0.789 0.21   1
## delightful      10 0.88 0.781 0.22   1
## pleasing        24 0.88 0.771 0.23   1
## pretty          25 0.85 0.726 0.27   1
## attractive       3 0.85 0.722 0.28   1
## satisfying      28 0.84 0.705 0.29   1
## beautiful        5 0.84 0.703 0.30   1
## inviting        18 0.83 0.687 0.31   1
## tasteful        30 0.83 0.684 0.32   1
## lovely          20 0.83 0.682 0.32   1
## harmonious      16 0.81 0.652 0.35   1
## engaging        12 0.80 0.647 0.35   1
## elegant         11 0.80 0.633 0.37   1
## exciting        14 0.79 0.622 0.38   1
## motivating      21 0.77 0.588 0.41   1
## wellDesigned    31 0.76 0.582 0.42   1
## interesting     17 0.74 0.543 0.46   1
## balanced         4 0.74 0.543 0.46   1
## fascinating     15 0.71 0.501 0.50   1
## sophisticated   29 0.71 0.500 0.50   1
## clean            6 0.67 0.449 0.55   1
## artistic         2 0.67 0.443 0.56   1
## organized       23 0.65 0.426 0.57   1
## creative         9 0.65 0.418 0.58   1
## colorHarmonious  8 0.64 0.406 0.59   1
## professional    26 0.60 0.355 0.64   1
## provoking       27 0.35 0.126 0.87   1
## cluttered        7 0.24 0.056 0.94   1
## 
##                  PA1
## SS loadings    18.14
## Proportion Var  0.59
## 
## Mean item complexity =  1
## Test of the hypothesis that 1 factor is sufficient.
## 
## The degrees of freedom for the null model are  465  and the objective function was  32.44
## The degrees of freedom for the model are 434  and the objective function was  6.31 
## 
## The root mean square of the residuals (RMSR) is  0.06 
## The df corrected root mean square of the residuals is  0.06 
## 
## Fit based upon off diagonal values = 0.99
## Measures of factor score adequacy             
##                                                    PA1
## Correlation of (regression) scores with factors   0.99
## Multiple R square of scores with factors          0.98
## Minimum correlation of possible factor scores     0.96

Factor Loadings for all images from the chosen FA method

  write.table(df,"generatedData-EFA/factorLoadings_all_images.tsv",row.names=FALSE,sep='\t')
  print(xtable(df),type="html")
terms PA1 Image 1 PA1 Image 2 PA1 Image 3 PA1 Image 4 PA1 Image 5 PA1 Image 6 PA1 Image 7 PA1 Image 8 PA1 Image 9 PA1 Image 10 PA1 Image 11 PA1 Image 12 PA1 Image 13 PA1 Image 14 PA1 Image 15
1 appealing 0.85 0.80 0.80 0.84 0.87 0.83 0.88 0.85 0.85 0.88 0.85 0.88 0.88 0.83 0.90
2 artistic 0.52 0.49 0.51 0.59 0.66 0.63 0.69 0.61 0.56 0.66 0.64 0.69 0.55 0.58 0.67
3 attractive 0.84 0.78 0.81 0.81 0.86 0.87 0.89 0.84 0.84 0.86 0.85 0.87 0.86 0.84 0.85
4 balanced 0.69 0.63 0.61 0.73 0.71 0.69 0.59 0.70 0.65 0.77 0.74 0.66 0.68 0.71 0.74
5 beautiful 0.84 0.77 0.76 0.79 0.84 0.78 0.87 0.81 0.76 0.82 0.85 0.85 0.78 0.82 0.84
6 clean 0.73 0.70 0.71 0.64 0.70 0.60 0.66 0.70 0.60 0.68 0.71 0.71 0.63 0.73 0.67
7 cluttered 0.30 -0.33 0.03 0.15 0.39 0.18 0.27 0.34 0.41 0.45 0.21 -0.05 0.12 0.05 0.24
8 colorHarmonious 0.65 0.59 0.63 0.63 0.64 0.63 0.48 0.55 0.43 0.62 0.51 0.62 0.43 0.64 0.64
9 creative 0.53 0.49 0.55 0.60 0.67 0.62 0.66 0.70 0.62 0.68 0.65 0.64 0.58 0.54 0.65
10 delightful 0.86 0.74 0.78 0.85 0.83 0.81 0.89 0.82 0.79 0.82 0.86 0.88 0.89 0.84 0.88
11 elegant 0.83 0.76 0.71 0.78 0.74 0.68 0.83 0.69 0.71 0.84 0.76 0.80 0.78 0.74 0.80
12 engaging 0.79 0.70 0.76 0.74 0.78 0.78 0.82 0.83 0.74 0.76 0.79 0.77 0.80 0.73 0.80
13 enjoyable 0.87 0.78 0.83 0.86 0.86 0.84 0.88 0.87 0.84 0.87 0.85 0.88 0.83 0.85 0.89
14 exciting 0.79 0.66 0.72 0.76 0.81 0.76 0.81 0.77 0.70 0.77 0.82 0.77 0.79 0.75 0.79
15 fascinating 0.68 0.64 0.73 0.77 0.70 0.72 0.80 0.71 0.72 0.66 0.73 0.77 0.76 0.70 0.71
16 harmonious 0.79 0.69 0.76 0.75 0.82 0.74 0.74 0.74 0.69 0.80 0.77 0.80 0.76 0.75 0.81
17 interesting 0.70 0.70 0.71 0.74 0.76 0.71 0.73 0.74 0.61 0.64 0.70 0.73 0.74 0.59 0.74
18 inviting 0.83 0.74 0.71 0.73 0.82 0.80 0.84 0.85 0.78 0.78 0.83 0.78 0.84 0.76 0.83
19 likable 0.91 0.79 0.88 0.87 0.86 0.84 0.90 0.88 0.84 0.86 0.85 0.89 0.87 0.87 0.89
20 lovely 0.85 0.75 0.78 0.82 0.80 0.77 0.83 0.81 0.74 0.81 0.86 0.86 0.83 0.79 0.83
21 motivating 0.74 0.65 0.71 0.77 0.83 0.78 0.84 0.75 0.75 0.77 0.78 0.71 0.83 0.76 0.77
22 nice 0.90 0.81 0.81 0.82 0.87 0.83 0.87 0.87 0.81 0.85 0.84 0.82 0.89 0.82 0.89
23 organized 0.59 0.61 0.62 0.74 0.67 0.59 0.55 0.60 0.59 0.66 0.64 0.66 0.65 0.62 0.65
24 pleasing 0.85 0.80 0.84 0.88 0.89 0.87 0.90 0.84 0.80 0.88 0.87 0.88 0.87 0.84 0.88
25 pretty 0.85 0.76 0.77 0.78 0.81 0.81 0.88 0.79 0.76 0.80 0.84 0.85 0.83 0.86 0.85
26 professional 0.63 0.67 0.52 0.61 0.62 0.53 0.60 0.46 0.50 0.61 0.52 0.67 0.67 0.62 0.60
27 provoking 0.17 0.20 0.22 0.28 0.28 0.33 0.19 0.37 0.32 0.27 0.40 0.32 0.22 0.22 0.35
28 satisfying 0.77 0.73 0.77 0.83 0.85 0.80 0.90 0.80 0.82 0.85 0.86 0.87 0.85 0.81 0.84
29 sophisticated 0.68 0.63 0.62 0.63 0.61 0.62 0.73 0.65 0.66 0.63 0.63 0.75 0.71 0.71 0.71
30 tasteful 0.78 0.64 0.68 0.72 0.77 0.78 0.80 0.81 0.81 0.80 0.82 0.76 0.81 0.77 0.83
31 wellDesigned 0.76 0.71 0.67 0.77 0.81 0.73 0.69 0.71 0.73 0.74 0.76 0.81 0.81 0.66 0.76

Terms for which all factor loadings are >.7

  remainingTerms <- df %>% filter_all(all_vars(. > 0.7))
  write.table(remainingTerms,"generatedData-EFA/factorLoadingsAbove_.7_all_images.tsv",row.names=FALSE,sep='\t')
  print(xtable(remainingTerms),type="html")
terms PA1 Image 1 PA1 Image 2 PA1 Image 3 PA1 Image 4 PA1 Image 5 PA1 Image 6 PA1 Image 7 PA1 Image 8 PA1 Image 9 PA1 Image 10 PA1 Image 11 PA1 Image 12 PA1 Image 13 PA1 Image 14 PA1 Image 15
1 appealing 0.85 0.80 0.80 0.84 0.87 0.83 0.88 0.85 0.85 0.88 0.85 0.88 0.88 0.83 0.90
2 attractive 0.84 0.78 0.81 0.81 0.86 0.87 0.89 0.84 0.84 0.86 0.85 0.87 0.86 0.84 0.85
3 beautiful 0.84 0.77 0.76 0.79 0.84 0.78 0.87 0.81 0.76 0.82 0.85 0.85 0.78 0.82 0.84
4 delightful 0.86 0.74 0.78 0.85 0.83 0.81 0.89 0.82 0.79 0.82 0.86 0.88 0.89 0.84 0.88
5 enjoyable 0.87 0.78 0.83 0.86 0.86 0.84 0.88 0.87 0.84 0.87 0.85 0.88 0.83 0.85 0.89
6 inviting 0.83 0.74 0.71 0.73 0.82 0.80 0.84 0.85 0.78 0.78 0.83 0.78 0.84 0.76 0.83
7 likable 0.91 0.79 0.88 0.87 0.86 0.84 0.90 0.88 0.84 0.86 0.85 0.89 0.87 0.87 0.89
8 lovely 0.85 0.75 0.78 0.82 0.80 0.77 0.83 0.81 0.74 0.81 0.86 0.86 0.83 0.79 0.83
9 nice 0.90 0.81 0.81 0.82 0.87 0.83 0.87 0.87 0.81 0.85 0.84 0.82 0.89 0.82 0.89
10 pleasing 0.85 0.80 0.84 0.88 0.89 0.87 0.90 0.84 0.80 0.88 0.87 0.88 0.87 0.84 0.88
11 pretty 0.85 0.76 0.77 0.78 0.81 0.81 0.88 0.79 0.76 0.80 0.84 0.85 0.83 0.86 0.85
12 satisfying 0.77 0.73 0.77 0.83 0.85 0.80 0.90 0.80 0.82 0.85 0.86 0.87 0.85 0.81 0.84